Superballistic characteristics in transient phonon ballistic-diffusive transport

Abstract

While diffusive, superdiffusive, and ballistic phonon transports have been widely investigated, the superballistic phenomenon, where the time index of the energy mean square displacement with respect to time is greater than 2, has been neither predicted nor observed. In this work, we report on the superballistic characteristics obtained from simulations of transient phonon ballistic-diffusive transport both during and after the input of a heat pulse into a nanoscale film. The superballistic behaviors are well described by a previously proposed model for electron wave packet spreading employing a point source and further explained by the superposition effect of heat pulses. The relative superposition time, a dimensionless parameter, is defined to describe the degree of the heat pulse superposition. The analysis of superballistic characteristics in this work is expected to guide experiments for detecting the phonon superballistic transport. Also, it provides a potential phenomenological description for the superballistic phenomena in more complex systems.